Acronym n/d-cupe
Name n/d-cupola prism,
n/d-prism atop 2n/d-prism
Segmentochoron display  
Circumradius sqrt[(5+2 cos(π d/n)-4 cos2(π d/n))/(6-8 cos2(π d/n))]
Lace city
in approx. ASCII-art
x-n/d-o  x-n/d-x	-- n/d-cupola
                
                
                
                
                
x-n/d-o  x-n/d-x	-- n/d-cupola

   |        +- 2n/d-prism
   +---------- n/d-prism
Especially tisdip (n=2,d=1)*   tricupe (n=3,d=1)   squacupe (n=4,d=1)   pecupe (n=5,d=1)   hicupe (n=6,d=1)*  
Confer
general polytopal classes:
segmentochora  

The height formula given below shows that only 2 < n/d < 6 is possible.
* The maximal height would be obtained at n/d = 2 with upright latteral triangles but then degenerate top base (and thus slightly different incidence matrix), the other extremal value n/d = 6 would generate a height of zero.


Incidence matrix according to Dynkin symbol

xx-n/d-ox xx&#x   (6/5<n/d<6 and n/d<>2)   → height = sqrt[1-1/(4 sin2(π d/n))]
(n/d-p || 2n/d-p)

o.-n/d-o. o.    | 2n  * |  2 1  2  0  0  0 | 1 2  2  1  2 0 0 0 | 1 1 2 1 0
.o-n/d-.o .o    |  * 4n |  0 0  1  1  1  1 | 0 0  1  1  1 1 1 1 | 0 1 1 1 1
----------------+-------+------------------+--------------------+----------
x.     .. ..    |  2  0 | 2n *  *  *  *  * | 1 1  1  0  0 0 0 0 | 1 1 1 0 0
..     .. x.    |  2  0 |  * n  *  *  *  * | 0 2  0  0  2 0 0 0 | 1 0 2 1 0
oo-n/d-oo oo&#x |  1  1 |  * * 4n  *  *  * | 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.x     .. ..    |  0  2 |  * *  * 2n  *  * | 0 0  1  0  0 1 1 0 | 0 1 1 0 1
..     .x ..    |  0  2 |  * *  *  * 2n  * | 0 0  0  1  0 1 0 1 | 0 1 0 1 1
..     .. .x    |  0  2 |  * *  *  *  * 2n | 0 0  0  0  1 0 1 1 | 0 0 1 1 1
----------------+-------+------------------+--------------------+----------
x.-n/d-o. ..    |  n  0 |  n 0  0  0  0  0 | 2 *  *  *  * * * * | 1 1 0 0 0
x.     .. x.    |  4  0 |  2 2  0  0  0  0 | * n  *  *  * * * * | 1 0 1 0 0
xx     .. ..&#x |  2  2 |  1 0  2  1  0  0 | * * 2n  *  * * * * | 0 1 1 0 0
..     ox ..&#x |  1  2 |  0 0  2  0  1  0 | * *  * 2n  * * * * | 0 1 0 1 0
..     .. xx&#x |  2  2 |  0 1  2  0  0  1 | * *  *  * 2n * * * | 0 0 1 1 0
.x-n/d-.x ..    |  0 2n |  0 0  0  n  n  0 | * *  *  *  * 2 * * | 0 1 0 0 1
.x     .. .x    |  0  4 |  0 0  0  2  0  2 | * *  *  *  * * n * | 0 0 1 0 1
..     .x .x    |  0  4 |  0 0  0  0  2  2 | * *  *  *  * * * n | 0 0 0 1 1
----------------+-------+------------------+--------------------+----------
x.-n/d-o. x.     2n  0 | 2n n  0  0  0  0 | 2 n  0  0  0 0 0 0 | 1 * * * *
xx-n/d-ox ..&#x   n 2n |  n 0 2n  n  n  0 | 1 0  n  n  0 1 0 0 | * 2 * * *
xx     .. xx&#x   4  4 |  2 2  4  2  0  2 | 0 1  2  0  2 0 1 0 | * * n * *
..     ox xx&#x   2  4 |  0 1  4  0  2  2 | 0 0  0  2  2 0 0 1 | * * * n *
.x-n/d-.x .x      0 4n |  0 0  0 2n 2n 2n | 0 0  0  0  0 2 n n | * * * * 1

xx-n/d-ox&#x || xx-n/d-ox&#x   (6/5<n/d<6 and n/d<>2)   → height = 1
(n/d-cu || n/d-cu)

o.-n/d-o.    || ..     ..    | n  * *  * | 2  2 1 0 0  0 0  0 0 0 | 1 2 1 2  2 0 0 0 0 0 0 0 | 1 1 2 1 0 0
.o-n/d-.o    || ..     ..    | * 2n *  * | 0  1 0 1 1  1 0  0 0 0 | 0 1 1 0  1 1 1 1 0 0 0 0 | 1 0 1 1 1 0
..     ..    || o.-n/d-o.    | *  * n  * | 0  0 1 0 0  0 2  2 0 0 | 0 0 0 2  2 0 0 0 1 2 1 0 | 0 1 2 1 0 1
..     ..    || .o-n/d-.o    | *  * * 2n | 0  0 0 0 0  1 0  1 1 1 | 0 0 0 0  1 0 1 1 0 1 1 1 | 0 0 1 1 1 1
-----------------------------+-----------+------------------------+--------------------------+------------
x.     ..    || ..     ..    | 2  0 0  0 | n  * * * *  * *  * * * | 1 1 0 1  0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo-n/d-oo&#x || ..     ..    | 1  1 0  0 | * 2n * *  * *  * * * * | 0 1 1 0  1 0 0 0 0 0 0 0 | 1 0 1 1 0 0
o.-n/d-o.    || o.-n/d-o.    | 1  0 1  0 | *  * n * *  * *  * * * | 0 0 0 2  2 0 0 0 0 0 0 0 | 0 1 2 1 0 0
.x     ..    || ..     ..    | 0  2 0  0 | *  * * n *  * *  * * * | 0 1 0 0  0 1 1 0 0 0 0 0 | 1 0 1 0 1 0
..     .x    || ..     ..    | 0  2 0  0 | *  * * * n  * *  * * * | 0 0 1 0  0 1 0 1 0 0 0 0 | 1 0 0 1 1 0
.o-n/d-.o    || .o-n/d-.o    | 0  1 0  1 | *  * * * * 2n *  * * * | 0 0 0 0  1 0 1 1 0 0 0 0 | 0 0 1 1 1 0
..     ..    || x.     ..    | 0  0 2  0 | *  * * * *  * n  * * * | 0 0 0 1  0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
..     ..    || oo-n/d-oo&#x | 0  0 1  1 | *  * * * *  * * 2n * * | 0 0 0 0  1 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..     ..    || .x     ..    | 0  0 0  2 | *  * * * *  * *  * n * | 0 0 0 0  0 0 1 0 0 1 0 1 | 0 0 1 0 1 1
..     ..    || ..     .x    | 0  0 0  2 | *  * * * *  * *  * * n | 0 0 0 0  0 0 0 1 0 0 1 1 | 0 0 0 1 1 1
-----------------------------+-----------+------------------------+--------------------------+------------
x.-n/d-o.    || ..     ..    | n  0 0  0 | n  0 0 0 0  0 0  0 0 0 | 1 * * *  * * * * * * * * | 1 1 0 0 0 0
xx     ..&#x || ..     ..    | 2  2 0  0 | 1  2 0 1 0  0 0  0 0 0 | * n * *  * * * * * * * * | 1 0 1 0 0 0
..     ox&#x || ..     ..    | 1  2 0  0 | 0  2 0 0 1  0 0  0 0 0 | * * n *  * * * * * * * * | 1 0 0 1 0 0
x.     ..    || x.     ..    | 2  0 2  0 | 1  0 2 0 0  0 1  0 0 0 | * * * n  * * * * * * * * | 0 1 1 0 0 0
oo-n/d-oo&#x || oo-n/d-oo&#x | 1  1 1  1 | 0  1 1 0 0  1 0  1 0 0 | * * * * 2n * * * * * * * | 0 0 1 1 0 0
.x-n/d-.x    || ..     ..    | 0 2n 0  0 | 0  0 0 n n  0 0  0 0 0 | * * * *  * 1 * * * * * * | 1 0 0 0 1 0
.x     ..    || .x     ..    | 0  2 0  2 | 0  0 0 1 0  2 0  0 1 0 | * * * *  * * n * * * * * | 0 0 1 0 1 0
..     .x    || ..     .x    | 0  2 0  2 | 0  0 0 0 1  2 0  0 0 1 | * * * *  * * * n * * * * | 0 0 0 1 1 0
..     ..    || x.-n/d-o.    | 0  0 n  0 | 0  0 0 0 0  0 n  0 0 0 | * * * *  * * * * 1 * * * | 0 1 0 0 0 1
..     ..    || xx     ..&#x | 0  0 2  2 | 0  0 0 0 0  0 1  2 1 0 | * * * *  * * * * * n * * | 0 0 1 0 0 1
..     ..    || ..     ox&#x | 0  0 1  2 | 0  0 0 0 0  0 0  2 0 1 | * * * *  * * * * * * n * | 0 0 0 1 0 1
..     ..    || .x-n/d-.x    | 0  0 0 2n | 0  0 0 0 0  0 0  0 n n | * * * *  * * * * * * * 1 | 0 0 0 0 1 1
-----------------------------+-----------+------------------------+--------------------------+------------
xx-n/d-ox&#x || ..     ..     n 2n 0  0 | n 2n 0 n n  0 0  0 0 0 | 1 n n 0  0 1 0 0 0 0 0 0 | 1 * * * * *
x.-n/d-o.    || x.-n/d-o.     n  0 n  0 | n  0 n 0 0  0 n  0 0 0 | 1 0 0 n  0 0 0 0 1 0 0 0 | * 1 * * * *
xx     ..&#x || xx     ..&#x  2  2 2  2 | 1  2 2 1 0  2 1  2 1 0 | 0 1 0 1  2 0 1 0 0 1 0 0 | * * n * * *
..     ox&#x || ..     ox&#x  1  2 1  2 | 0  2 1 0 1  2 0  2 0 1 | 0 0 1 0  2 0 0 1 0 0 1 0 | * * * n * *
.x-n/d-.x    || .x-n/d-.x     0 2n 0 2n | 0  0 0 n n 2n 0  0 n n | 0 0 0 0  0 1 n n 0 0 0 1 | * * * * 1 *
..     ..    || xx-n/d-ox&#x  0  0 n 2n | 0  0 0 0 0  0 n 2n n n | 0 0 0 0  0 0 0 0 1 n n 1 | * * * * * 1

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